Enumerating matchings is a classical problem in the field of enumeration algorithms. There are polynomial-delay enumeration algorithms for several settings, such as enumerating perfect matchings, maximal matchings, and (weighted) matchings in specific orders. In this paper, we present polynomial-delay enumeration algorithms for maximal matchings with cardinality at least given threshold $t$. Our algorithm enumerates all such matchings in $O(nm)$ delay with exponential space, where $n$ and $m$ are the number of vertices and edges of an input graph, respectively. We also present a polynomial-delay and polynomial-space enumeration algorithm for this problem. As a variant of this algorithm, we give an algorithm that enumerates all maximal matchings in non-decreasing order of its cardinality and runs in $O(nm)$ delay.

翻译：点算算法领域的一个典型问题是计算匹配。 在多个设置中, 有多个多数值- 延迟查点算法, 例如在特定顺序中列出完美匹配、 最大匹配和( 加权) 匹配。 在本文中, 我们提出多数值- 延迟查点算法, 用于最小匹配, 至少给定临界值 $t 。 我们的算法用指数空间的延迟用$( n) 来罗列所有这些匹配, 指数空间的延迟时间分别为 $( n) 和 $( $) 。 我们还为此问题提出了一个多数值- 边和多数值- 空间查点算法 。 作为这种算法的一种变式, 我们给出一种算法, 将所有最大匹配值都用非确定基值顺序来计算, 以 $( n) 美元 来计算, 并运行 $O ( n) 的延迟 。